Marginals of a spherical spin glass model with correlated disorder

Abstract

In this paper we prove the weak convergence, in the high-temperature phase, of the finite marginals of the Gibbs measure associated to a symmetric spherical spin glass model with correlated couplings towards an explicit asymptotic decoupled measure. We also provide upper bounds for the rate of convergence in terms of the one of the energy per variable. Furthermore, we establish a concentration inequality for bounded functions in a subset of the high-temperature phase. These results are exemplified by analysing the asymptotic behaviour of the empirical mean of coordinate-wise functions of samples from the Gibbs measure of the model.